An Average Solvent Electrostatic Configuration Protocol for QM/MM Free Energy Optimization: Implementation and Application to Rhodopsin Systems.

A novel atomistic methodology to perform free energy geometry optimization of a retinal chromophore covalently bound to any rhodopsin-like protein cavity is presented and benchmarked by computing the absorption maxima wavelengths (λ) of distant rhodopsin systems. The optimization is achieved by computing the Nagaoka's Free Energy Gradient (FEG) within an Average Solvent Electrostatic Configuration (ASEC) atomistic representation of the thermodynamic equilibrium and minimizing such quantity via an iterative procedure based on sequential classical MD and constrained QM/MM geometry optimization steps. The performance of such an ASEC-FEG protocol is assessed at the CASPT2//CASSCF/Amber level by reproducing the λ values observed for 12 mutants of redesigned human cellular retinol binding protein II (hCRBPII) systems; a set of 10 distant wild-type rhodopsins from vertebrates, invertebrates, eubacteria, and archaea organisms; and finally a set of 10 rhodopsin mutants from an eubacterial rhodopsin. The results clearly show that the proposed protocol, which can be easily extended to any protein incorporating a covalently bound ligand, yields correct λ trends with limited absolute errors.